Learn Hardcore German: Vorher war nirgendwo Platz, nachher finden wir bestimmt einen Tisch. - Beforehand there was nowhere to sit, afterwards we will surely find a table.

vorher = beforehand/earlier (relative to a previously mentioned or understood reference point).
nachher = afterwards/later (often implies “a bit later,” commonly the same day).
danach = after that (explicitly refers back to a specific event mentioned).
später = later (more general, not tied to a specific prior event).
hinterher = afterward/after it (often spatial or following someone/something).

In this sentence, vorher … nachher is a neat before–after pairing.

Why is it nachher finden wir and not nachher wir finden?

German main clauses follow the V2 (verb-second) rule. If something other than the subject is in first position (here: nachher), the finite verb must come next, and the subject follows it: Nachher finden wir …. If the subject were first, you’d say Wir finden nachher ….

Why is the present tense (finden) used for a future meaning?

German very often uses the present tense to talk about the future when there’s a time expression like nachher, morgen, etc. You could use werden + infinitive, but it’s not required here.

Is Nachher werden wir bestimmt einen Tisch finden also correct?

Yes. It’s fully correct and a bit more explicitly “future.” The original with simple present is slightly more casual/natural in everyday speech when the timeframe is clear.

Does bestimmt mean “definitely” or “probably”?

It straddles both. In many contexts it means “definitely/certainly.” In everyday speech, especially when reassuring someone, it can sound like “I’m sure we’ll probably manage.” Stronger certainty would be sicher or ganz sicher; weaker would be wahrscheinlich.

Where does bestimmt belong in the sentence? Can it move?

Preferred positions:

After the subject: Wir bestimmt rarely goes directly after the subject with simple verbs, so better is: Wir finden bestimmt einen Tisch.
After the finite verb: Nachher finden wir bestimmt einen Tisch. With werden it often sits between werden and the main verb: Wir werden bestimmt einen Tisch finden. Avoid: Wir finden einen Tisch bestimmt (possible but marked/odd unless you’re stressing the object).

Why is there a comma between the two parts without a conjunction like “and” or “but”?

German allows two independent main clauses to be joined with just a comma (asyndetic coordination). English usually requires a conjunction or a semicolon. You could add aber, und, or und dann, but the simple comma is fine in German: Vorher …, nachher ….

What does nirgendwo mean? Is it the same as nirgends?

nirgendwo = nowhere (standard).
nirgends = also nowhere (equally standard, often a bit more colloquial/shorter). Don’t use the nonstandard hybrid nirgendswo. For direction, use nirgendwohin (to nowhere); for source, nirgendwoher (from nowhere).

Why is there no article before Platz in war nirgendwo Platz?

Platz here means “room/space” (an uncountable/mass-like use), and German often uses a zero article for such predicate nouns with sein: Hier ist Platz = “There is room here.” You’ll also hear the expletive version: Es ist/war nirgendwo Platz.

Could I say Es gab nirgendwo Platz or Es war nirgends Platz instead?

Yes:

Es gab nirgendwo Platz emphasizes existence/availability (there was no space anywhere).
Es war nirgends/nirgendwo Platz is very idiomatic and common. All are acceptable; nuances are minimal in everyday use.

Why is it einen Tisch and not ein Tisch or einem Tisch?

Tisch is masculine. As the direct object (accusative), the indefinite article is einen:

Nominative: ein Tisch
Accusative: einen Tisch
Dative: einem Tisch
Genitive: eines Tisches

Can I use bevor instead of vorher here?

Not directly. bevor introduces a subordinate clause with its own subject and verb:

With bevor: Bevor kamen wir, war nirgendwo Platz is ungrammatical because bevor needs a clause: Bevor wir kamen, war nirgendwo Platz.
vorher is an adverb and starts a main clause: Vorher war nirgendwo Platz.

Is zuvor a good alternative to vorher?

Yes, zuvor is a near-synonym, a bit more formal/literary. Zuvor war nirgendwo Platz sounds a touch elevated compared to Vorher ….

Why use Platz first and then einen Tisch? Isn’t that mixing “space” and “table”?

It’s natural: first you state there was no space available (Platz = “room/space”), then you predict you’ll actually get a seat by finding einen Tisch (a physical table). You could also say einen Platz (a seat/spot), but in restaurants einen Tisch is very idiomatic.

Any pronunciation tips for nachher and vorher?

nachher: the ch is the velar (like in Bach), and the h indicates the vowel is long: [ˈnaːx.heːɐ̯].
vorher: long o in vor, long e in her: [ˈfoːʁ.heːɐ̯].